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The hybrid Monte Carlo algorithm on Hilbert space

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Stuart, A. M. (2010) The hybrid Monte Carlo algorithm on Hilbert space. In: Stochastic Partial Differential Equations (SPDEs) : Approximation, Asymtotics and Computation. , Cambridge, 28 Jun-02 Jul 2010 (Unpublished)

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Official URL: http://www.newton.ac.uk/programmes/SPD/spdw04p.htm...

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Abstract

Hybrid Monte Carlo methods are a class of algorithms for sampling probability measures defined via a density with respect to Lebesgue measure. However, in many applications the probability measure of interest is on an infinite dimensional Hilbert space and is defined via a density with respect to a Gaussian measure. I will show how the Hybrid Monte Carlo methodology can be extended to this Hilbert space setting. A key building block is the study of measure preservation properties for certain semilinear partial differential equations of Hamiltonian type, and approximation of these equations by volume-preserving integrators. Joint work with A. Beskos (UCL), F. Pinski (Cincinnati) and J.-M. Sanz-Serna (Valladolid).

Item Type: Conference Item (Paper)
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science > Mathematics
Official Date: 30 June 2010
Dates:
DateEvent
30 June 2010Completion
Status: Not Peer Reviewed
Publication Status: Unpublished
Version or Related Resource: Stuart, A. M. (2010). The hybrid Monte Carlo algorithm on Hilbert space. In: Highly Oscillatory Problems : From Theory to Applications. Cambridge, 15 Sep 2010.
Conference Paper Type: Paper
Title of Event: Stochastic Partial Differential Equations (SPDEs) : Approximation, Asymtotics and Computation.
Type of Event: Conference
Location of Event: Cambridge
Date(s) of Event: 28 Jun-02 Jul 2010

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